The value of $\tan 81^{\circ}-\tan 63^{\circ}-\tan 27^{\circ}+\tan 9^{\circ}$ is
$0$
$2$
$3$
$4$
$cosec^2\theta $ = $\frac{4xy}{(x +y)^2}$ is true if and only if
If $\cos A = \cos B\,\,\cos C$and $A + B + C = \pi ,$ then the value of $\cot \,B\,\cot \,C$ is
Let $\alpha ,\beta $ be such that $\pi < (\alpha - \beta ) < 3\pi $. If $\sin \alpha + \sin \beta = - \frac{{21}}{{65}}$ and $\cos \alpha + \cos \beta = - \frac{{27}}{{65}},$ then the value of $\cos \frac{{\alpha - \beta }}{2}$ is
If $\theta = 3\, \alpha$ and $sin\, \theta =$ $\frac{a}{{\sqrt {{a^2}\,\, + \,\,{b^2}} }}$. The value of the expression , $a \,cosec\, \alpha - b \,sec\, \alpha$ is
For $A = 133^\circ ,\;2\cos \frac{A}{2}$ is equal to